A Counter-intuitive PYTHAGOREAN SURPRISE

Imagine a tightly stretched rope from one end of the field to be 100m; so the length of the rope is 100m. Now replace this rope by one that is slightly longer, say by 20 cm. There is some slack in the rope, so we should be able to lift the midpoint of the rope to some height. Imagine pinching the rope at its midpoint and raising the rope till it is taut. Question: To what height can you raise the midpoint?  

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